A258979 Numbers n such that 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 is prime.

1, 4, 6, 9, 11, 12, 14, 15, 23, 27, 29, 32, 43, 54, 56, 61, 64, 67, 73, 87, 95, 106, 109, 128, 134, 138, 146, 154, 163, 165, 171, 172, 197, 213, 235, 252, 253, 258, 259, 273, 274, 290, 300, 301, 303, 307, 314, 326, 330, 335, 358, 387, 393, 394, 403, 404, 412

Offset: 1

Author

Robert Price, Jun 15 2015

Keywords

• nonn

Links

• Robert Price, Table of n, a(n) for n = 1..932
• OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Crossrefs

Cf. A000203, A258978, A258980.

Programs

Magma

[n: n in [1..500] | IsPrime(1 + DivisorSigma(1, n) + DivisorSigma(1, n)^2 + DivisorSigma(1, n)^3 + DivisorSigma(1, n)^4)]; // Vincenzo Librandi, Jun 16 2015

Maple

with(numtheory): A258979:=n->`if`(isprime(1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4), n, NULL): seq(A258979(n), n=1..1000); # Wesley Ivan Hurt, Jul 09 2015

Mathematica

Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #] + DivisorSigma[1, #]^2 + DivisorSigma[1, #]^3 + DivisorSigma[1, #]^4] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[5, DivisorSigma[1, #]]] &]
Select[Range[10000],PrimeQ[Total[DivisorSigma[1,#]^Range[0,4]]]&] (* Harvey P. Dale, Aug 17 2015 *)

PARI

is(n)=my(s=sigma(n)); isprime(s^4+s^3+s^2+s+1) \\ Charles R Greathouse IV, May 22 2017